Question

If A = `[(1, 0, 0),(0, 1, 0),("a", "b", -1)]` and I is the unit matrix of order 3, then A² + 2A⁴ + 4A⁶ is equal to ______.

Options

• 7A⁸

• 7A⁷

• 8I

• 6I

Answer 1

If A = `[(1, 0, 0),(0, 1, 0),("a", "b", -1)]` and I is the unit matrix of order 3, then A² + 2A⁴ + 4A⁶ is equal to 7A⁸.

Explanation:

A² = `[(1, 0, 0),(0, 1, 0),("a", "b", -1)][(1, 0, 0),(0, 1, 0),("a", "b", -1)] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`

A² = A⁴ = A⁶ = I₃

`\implies` A² + 2A⁴ + 4A⁶

= `[(1, 0, 0),(0, 1, 0),(0, 0, 1)] + [(2, 0, 0),(0, 2, 0),(0, 0, 2)] + [(4, 0, 0),(0, 4, 0),(0, 0, 4)]`

= `[(7, 0, 0),(0, 7, 0),(0, 0, 7)]`

= 7I₃

= 7A⁸